Precalculus (6th Edition) Blitzer

by
Blitzer, Robert F.

Published by
Pearson

ISBN 10:
0-13446-914-3

ISBN 13:
978-0-13446-914-0

Chapter P - Section P.4 - Polynomials - Exercise Set - Page 56: 75

Answer

$9x^2-25y^2+42x+49$

Work Step by Step

The given expression can be written as:
$[(3x+7)-5y][(3x+7)+5y].$
The expression above is of the form $(a-b)(a+b)$.
RECALL:
(1) $(a-b)(a+b) = a^2-b^2$
(2) $(a+b)^2=a^2+2ab+b^2$
Multiply the expression using formula (1) above with $a=3x+7$ and $b=5y$ to obtain:
$=(3x+7)^2 - (5y)^2
\\=(3x+7)^2-25y^2$
Square the binomial using formula (2) with $a=3x$ and $b=7$ above to obtain:
$=(3x)^2+2(3x)(7)+7^2-25y^2
\\=9x^2+42x+49-25y^2
\\=9x^2-25y^2+42x+49$